Semisimple Operator and Semisimple Class for Rings  

环的半单算子与半单类

作　　者：胡长流[1] 田震[1] 

机构地区：[1]河南大学数学系

出　　处：《Chinese Quarterly Journal of Mathematics》1991年第1期68-74,共7页数学季刊（英文版）

摘　　要：For an arbitrary class of rings M, we have studied, in this paper, some necessary and sufficient conditions for ψM to be closed under homomorphic images or essential extensions, or to be a semisimple class or hereditary class. The main results are: Theorem 4.1 For an arbitrary class of rings M, the following are equivalent: (1) M is a semisimple class; (2) ψM = ψuψM; (3) M~*=(uψM)~*; (4) M^(**)■M~*■(uψM)~*. Theorem 4.3 For an arbitray class of rings M, the follawing are equivalent: (1) ψM is the semisimple class of a hereditary radical; (2) ψM is an essentially closed semisimple class; (3) M~*=(uψM)~* and M~* is essentially hereditary; (4) M~*=(uψM)~* and uψM is essentially hereditary; (5)M~*=(uψM)~* and ψM is essentially closed.

关 键 词：环类 半单算子 半单类 

分 类 号：O153.3[理学—数学]